Ok, a little bit of an update: The Steering Column Combo Switch (Which contains the blinker, brights, lights and wipers switch) is apparently extremely dirty on the inside. After blowing out the blinker switch part with some electronics cleaner and moving the switch back and forth a good bit, she works much more reliably. Definitely need to replace all the bulbs so I agree with you there. We did some testing and found she's producing the right voltage under load and idle that she's supposed to be, so it may be that the dirt in the switches themselves is causing a short that's making everything go haywire. I'm gonna do an even more thorough cleaning of the combo switches and see if I can't tighten any loose ends for the switch and see what happens there.

Now I just have to make sure her timing's right and get the carbs fixed, lol. Gotta love old cars, but at least it's easy to figure out what the problem is.